Steady State Error (page 3)
Chapter 7 covers dealing with steady state error. We only spend one day on this topic. We will use it in designing controllers twice more later in the quarter. Here's the topic in a nutshell.
The core tool for you to use is Table 7.2 on page 382. The table is for use with unity feedback systems, i.e.
In the above system, H = 1. If you have a non-unity feedback system, there is an easy way to convert into an equivalent unity feedback system. Section 7.6 in the book discusses how to do this.
ess depends on the "type" of G. To get the "type" of a transfer function count the number of free s's in its denominator. Free s's are s's that are NOT part of a first or second order component.
E.g.
is a type 1 system because there is one free integrator (the s by itself) in the denominator.
is a type 0 system.
is a type 2 system. Note two things: 1) an s2 can be factored out of the terms in the denominator and 2) the (s+6) in the numerator (the zero) has absolutely no effect on determining system type.
Note also that to determine system type, use the open-loop transfer function in a unity feedback system. Do not use the closed-loop transfer function nor G in a system where H is not equal to 1.